Hybrid estimators for small diffusion processes based on reduced data

Yusuke Kaino () and Masayuki Uchida
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Yusuke Kaino: Osaka University
Masayuki Uchida: Osaka University

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 7, No 1, 745-773

Abstract: Abstract We deal with the Bayes type estimators and the maximum likelihood type estimators of both drift and volatility parameters for small diffusion processes defined by stochastic differential equations with small perturbations from high frequency data. From the viewpoint of numerical analysis, initial Bayes type estimators for both drift and volatility parameters based on reduced data are required, and adaptive maximum likelihood type estimators with the initial Bayes type estimators, which are called hybrid estimators, are proposed. The asymptotic properties of the initial Bayes type estimators based on reduced data are derived and it is shown that the hybrid estimators have asymptotic normality and convergence of moments. Furthermore, a concrete example and simulation results are given.

Keywords: Bayes type estimator; Convergence of moments; Diffusion process; Discrete time observations; Maximum likelihood type estimator; Small dispersion parameters; Primary 62F12; 62M05; Secondary 60J60 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00184-018-0657-0

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